# how to find log and antilogs of +ve and -ve number

### Asked by mangesh | 25th Jun, 2016, 01:13: PM

###
The **logarithm** of a number is the exponent to which another fixed value, the base must be raised to produce that number.

To simplify difficult calculations, logarithms is a good tool.

These tables listed the values of log_{b}(x) and b^{x} for any number x in a certain range, at a certain precision, for a certain base b (usually b = 10).

For example, consider the number 567894.

logarithms of the number 567894 = log(567894).

The number of digits in the given number is 6.

Therefore the characteristic of the given number is 6 - 1 = 5.

Now let us find the mantissa part of the number 567894.

From the table, find the row with 56 and then under column 7, the value is 7536 and plus the value under column 8 is 6.

Hence the mantissa is 7536+6=7542

Now add the characteristic and mantissa.

Thus log(567894)=5 + 0.7542 =** 5.7542**

**Logarithm of negative number is not defined.**

Consider the following **antilog **table.

1) Now lets see antilog of 2.6992 .

The number before the decimal point is 2, so the decimal point will be after the first 3 digits.

From the antilog table, read off the row for .69 and column of 9; the number given in the table is 5000. The mean difference in the same row and under the column 2 is 2. To get the inverse of mantissa add 5000 + 2 = 5002.

Now place a decimal point after the first 3 digits and you get the number 500.2

Thus antilog 2.6992 = **500.2**

**Remember that the decimal part of the number for which you are seeing the antilog must be positive. If it's not, then you need to make it positive.**

2) e.g. for seeing antilog(-1.723)

write

-1.723

=-1+(-0.723)

=-1+ **(-1+1**-0.723)

= -2+0.277

Now see the antilogtable entry for .27 under the column 7

That wil come out to be 1892

Since the integral part is -2, (a negative number )

We follow the rule that there will be one zero (2-1=1) after the decimal point and then the antilog entry.

So antilog(-1.723) = **0.01892**

The **logarithm** of a number is the exponent to which another fixed value, the base must be raised to produce that number.

To simplify difficult calculations, logarithms is a good tool.

These tables listed the values of log_{b}(x) and b^{x} for any number x in a certain range, at a certain precision, for a certain base b (usually b = 10).

For example, consider the number 567894.

logarithms of the number 567894 = log(567894).

The number of digits in the given number is 6.

Therefore the characteristic of the given number is 6 - 1 = 5.

Now let us find the mantissa part of the number 567894.

From the table, find the row with 56 and then under column 7, the value is 7536 and plus the value under column 8 is 6.

Hence the mantissa is 7536+6=7542

Now add the characteristic and mantissa.

Thus log(567894)=5 + 0.7542 =** 5.7542**

**Logarithm of negative number is not defined.**

Consider the following **antilog **table.

1) Now lets see antilog of 2.6992 .

The number before the decimal point is 2, so the decimal point will be after the first 3 digits.

From the antilog table, read off the row for .69 and column of 9; the number given in the table is 5000. The mean difference in the same row and under the column 2 is 2. To get the inverse of mantissa add 5000 + 2 = 5002.

Now place a decimal point after the first 3 digits and you get the number 500.2

Thus antilog 2.6992 = **500.2**

**Remember that the decimal part of the number for which you are seeing the antilog must be positive. If it's not, then you need to make it positive.**

2) e.g. for seeing antilog(-1.723)

write

-1.723

=-1+(-0.723)

=-1+ **(-1+1**-0.723)

= -2+0.277

Now see the antilogtable entry for .27 under the column 7

That wil come out to be 1892

Since the integral part is -2, (a negative number )

We follow the rule that there will be one zero (2-1=1) after the decimal point and then the antilog entry.

So antilog(-1.723) = **0.01892**

### Answered by Prachi Sawant | 27th Jun, 2016, 11:08: AM

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